Intensive and Extensive Properties

Introduction

If you cut a gold bar in half, each half has half the mass and half the volume — but each is still gold with the same colour, density and melting point. Some properties change with the amount of material, and some do not. Chemists call these extensive and intensive properties. The distinction explains why density and melting point are so useful for identification, while mass is not.

Core explanation

Extensive properties depend on how much of the substance is present. If the amount doubles, the property doubles. Examples: - mass - volume - length - the total heat energy needed to warm a sample - the total amount of energy released when a fuel burns

Intensive properties do not depend on the amount. A drop of water and a swimming pool of water share the same values. Examples: - density - melting point and boiling point - temperature - colour - hardness - concentration of a solution - electrical conductivity (as a material property)

Ratios of extensive properties are intensive. Mass and volume are both extensive, but density = mass ÷ volume is intensive: doubling the sample doubles both mass and volume, and the ratio stays the same. Many useful intensive properties are built this way, such as "energy released per gram" for fuels.

Why intensive properties identify substances. Because an intensive property has the same value whatever the sample size, it can be compared directly with a data table. Knowing that a sample has a mass of 50 g tells you nothing about what it is; knowing that it has a density of 8.96 g/cm³ and melts at 1085 °C points strongly to copper.

Temperature is intensive. Pouring two cups of water at 60 °C into one jug gives water at 60 °C, not 120 °C. The total energy content doubles (extensive) but the temperature does not.

Step-by-step reasoning

To classify a property:

1. Imagine taking a sample and then a sample twice as large. 2. Ask: does the value of the property double (or change)? 3. If it changes with the amount, it is extensive. 4. If it stays the same, it is intensive.

Visual explanation

Property Small sample Double sample Type --- --- --- --- Mass 10 g 20 g Extensive Volume 3.7 cm³ 7.4 cm³ Extensive Density 2.70 g/cm³ 2.70 g/cm³ Intensive Melting point 660 °C 660 °C Intensive Colour Silvery Silvery Intensive

(Aluminium samples.)

Real-world analogy

The price you pay for fruit is extensive — more fruit costs more. The price per kilogram is intensive — it is the same whether you buy one apple or a whole crate. Intensive properties are like unit prices: they describe the kind of thing rather than how much of it you have.

Real-world example

Fuel companies compare fuels using energy released per kilogram (an intensive property), for example about 46 MJ/kg for petrol. The total energy in a tank is extensive and depends on how much fuel it holds. Engineers designing a car need both: the intensive value to choose a fuel and the extensive value to decide the tank size.

Why?

Why is concentration intensive, even though it involves an amount? Concentration is the amount of solute divided by the volume of solution. If you pour half of a solution into another glass, each glass has half the solute and half the volume, so the concentration in each is unchanged.

Common misconception

"Temperature and heat are the same thing." Temperature is intensive; the total heat energy stored is extensive. A bathtub of warm water at 40 °C contains far more heat energy than a cup of boiling water at 100 °C, even though its temperature is lower.

Worked example

Question: Classify each as intensive or extensive: (a) boiling point of ethanol; (b) the volume of ethanol in a bottle; (c) the density of ethanol; (d) the energy released when all the ethanol in the bottle burns.

Reasoning: (a) and (c) are the same for any amount. (b) and (d) grow with the amount of ethanol.

Answer: (a) intensive; (b) extensive; (c) intensive; (d) extensive.

Quick check

1. Is mass intensive or extensive? Answer: Extensive, because it depends on the amount of substance.

Exam focus

Learn the definitions and several examples of each. Explain density's classification by noting that it is a ratio of two extensive properties. Link intensive properties to identifying substances in "why is density useful?" questions.

Advanced insight

In thermodynamics, extensive quantities such as energy, enthalpy and entropy are often converted to intensive ones by dividing by the amount of substance (per mole) or by mass (per gram). Molar and specific quantities are the intensive forms tabulated in data books.

Summary

Extensive properties, such as mass, volume and total energy, depend on the amount of substance. Intensive properties, such as density, melting point, boiling point, temperature and colour, do not. Ratios of extensive properties are intensive. Intensive properties are the ones used to identify substances.

Practice questions

1. A 2 kg block and a 5 kg block of iron are compared. Which properties are the same for both? Answer: Intensive properties such as density, melting point, colour and hardness. 2. Why is volume not useful for identifying a substance? Answer: It is extensive: it depends on how much of the substance is present, not on what it is. 3. Two 100 mL portions of water at 25 °C are mixed. What is the temperature of the mixture, and why? Answer: 25 °C, because temperature is an intensive property and does not add. 4. Explain why density is intensive although mass and volume are extensive. Answer: Doubling the sample doubles both mass and volume, so their ratio (density) stays the same.